An analytical mathematical modeling to extract the parameters of solar cell from implicit equation to explicit form

Metaheuristic Algorithm for Photovoltaic Parameters: Comparative Study and Prediction with a Firefly Algorithm

“…Least squares and Newton-Raphson method [29] Iterative curve fitting [30] Lambert W-functions [20,[31][32][33][34][35] Integral-based linear least square identification method [36,37] Linear interpolation/extrapolation [38] Chebyshev polynomials [39] Taylor's series expansion [40] Padé approximants [41] Symbolic function [42] Analytical mathematical method [43][44][45] Simple methods based on measured points [46] Metaheuristic methods are powerful in local searches, but they tend to get trapped in locally optimal values and depend on the photovoltaic module's manufacturer's data such as open circuit, short circuit, and maximum power points. Since the photovoltaic cell has triple non-linearity in current-voltage, power-voltage and in intrinsic parameters, deterministic methods cannot extract parameters accurately based on current, voltage and current derivatives with respect to the voltage at short circuit current, maximum power and open circuit voltage.…”

Non-Iterative Methods for the Extraction of the Single-Diode Model Parameters of Photovoltaic Modules: A Review and Comparative Assessment

“…}; the calculation formula is given in Appendix A. The remaining parameters R sh , I s and I ph are found by the previous alternatives' Equations (40), (38) and (24). Please note that in this paper, the same diode factor is used for all PV technologies.…”

“…This class achieves generally high accuracy but suffers from initialization and convergence issues, high calculation cost and solution suboptimality [1,[11][12][13]. The non-iterative (or explicit or direct or analytical) methods employ a set of equations as well, but are solved symbolically/explicitly (no iterations) resulting in simpler formulation and implementation [12,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. These approaches are essentially variations of the numerical class that employ a series of simplifications and empirical observations to achieve explicit formulation.…”

“…For some methods, the datasheet information suffices (e.g., SC, OC, and MPP data, temperature coefficients etc.) [12,15,17,[20][21][22][25][26][27], while others require additional operating points or/and the slope of the I-V curve at SC or OC [14,16,18,19,23,24]. Generally, the former cases are preferable as they can be applied more easily and universally, not necessitating extra measurements [19,27,36].…”

“…To shed some light on these topics, this paper performs a comprehensive review and comparison of the non-iterative parameter extraction methods that are based on the single-diode PV model. Seventeen such methods are identified dating since 1984 [12,[14][15][16][17][18][19][20][21][22][23][24][25][26][27], all of which are implemented and assessed on a common set of I-V curves provided by National Renewable Energy Laboratories (NREL) [42]. This dataset contains 1,025,665 I-V curves measured over a one-year period in the USA for 22 PV modules under a wide range of irradiance and temperature conditions.…”